6 papers
Global hypoellipticity for perturbations of complex vector fields on the torus
Maria V. Bartmeyer, Paulo L. Dattori da Silva, Rafael B. Gonzalez
We apply Krönecker's approximation theorem to measure (in a topological sense) a set of constants which turn a vector field into a non-globally hypoelliptic operator. We present s…
Piecewise Smooth Dynamical Systems Regularized by Convolution
Claudio A. Buzzi, Daniel Panazzolo, Paulo R. da Silva
We present a general regularization procedure for piecewise smooth vector fields whose discontinuity locus is a variety of normal crossings type. We show that such regularization c…
Complex potentials and holomorphic differential equations
Gabriel Rondón, Paulo R. da Silva
A complex potential is a holomorphic function whose real and imaginary parts generate a pair of orthogonal foliations, representing the equipotential…
Directional Poincaré inequality on compact Lie groups
Paulo L. Dattori da Silva, André Pedroso Kowacs
We extend the directional Poincaré inequality on the torus, introduced by Steinerberger in [Ark. Mat. 54 (2016), pp. 555--569], to the setting of compact Lie groups. We provide ne…
On the Piecewise Holomorphic Systems with Three Zones
Carlos Vinicius das Neves Silva, Paulo Ricardo da Silva
We study piecewise-smooth systems with three zones, , whose discontinuity set consists either of a pair of parallel lines or a pair of circles t…
Diagonal systems of differential operators on compact Lie groups
Paulo L. Dattori da Silva, Alexandre Kirilov, Ricardo Paleari da Silva
We investigate the global hypoellipticity and global solvability of systems of left-invariant differential operators on compact Lie groups. Focusing on diagonal systems, we establi…